@Article{JNMA-1-513,
author = {Pan , XiaZheng , Zuohuan and Zhou , Zhe},
title = {Ergodic Behaviour of Nonconventional Ergodic Averages for Commuting Transformations},
journal = {Journal of Nonlinear Modeling and Analysis},
year = {2021},
volume = {1},
number = {4},
pages = {513--525},
abstract = {<p style="text-align: justify;">Based on T. Tao&#39;s celebrated result on the norm convergence of
multiple ergodic averages for commuting transformations, we find that there
is a subsequence which converges almost everywhere. Meanwhile, we obtain
the ergodic behaviour of diagonal measures, which indicates the time average
equals the space average. According to the classification of transformations,
we also give several different results. Additionally, on the torus&nbsp;$\mathbb{T}^d$ with special
rotation, we prove the pointwise convergence in&nbsp;$\mathbb{T}^d$&nbsp;, and get a result for ergodic
behaviour.</p>},
issn = {2562-2862},
doi = {https://doi.org/10.12150/jnma.2019.513},
url = {http://global-sci.org/intro/article_detail/jnma/18837.html}
}